If ${N_a} = \{ an : n \in N \}$,then ${N_3} \cap {N_4} = $

Along the $X$-axis,three charges $\frac{q}{2}, -q$ and $\frac{q}{2}$ are placed at $x=0, x=a$ and $x=2a$ respectively. The resultant electric potential at $x=a+r$ (if $a \ll r$) is: ($\varepsilon_0$ is the permittivity of free space)

$A$ conducting rod of length $\ell$ is moving with velocity $v$ in a uniform magnetic field $B$ directed into the plane of the paper,as shown in the diagram. Which end of the rod is at a lower potential?

$A$ Zener diode,having a breakdown voltage equal to $15\, V$,is used in a voltage regulator circuit as shown in the figure. The current through the Zener diode is.....$mA$.

The equation $16 x^2+y^2+8 x y-74 x-78 y+212=0$ represents:

The proposition $(\sim p) \vee (p \wedge \sim q)$ is equivalent to: